Question

A can finish a work in 20 days and B can finish the same work in 30days , A atarted the workband after 15 days B joined him . How many days they work together​

Answer 1

Question:-

A can finish a work in 20 days and B can finish the same work in 30 days , A started the work and after 15 days B joined him . How many days they work together?

Required Answer:-

Given:-

• a can finish the work in 20 days.
• B can finish the work in 30 days.
• A worked 15 days alone until B joined him.

To Find:-

• Number of days A and B worked together.

Solution:-

First we have to know that, if a person can finish a whole work in p days, then his 1 day working part will be 1/p

As we were given:-

In 20 days A finishes 1 (whole) part of work

∴ In 1 day A finishes 1/20 part of work.

Similarly,

In 30 days B finishes 1 (whole) part of work

∴ In 1 day B finishes 1/30 part of work.

Now,

1 day's work of A and B = 1/20 + 1/30 = (3+2) /60 = 5/60 = 1/12

Let us assume that they work together for x days.

In 1 day A+B can do 1/12 part of work

∴ In x days A+B can do x × 1/12 = x/12 part of work

Now, as A has completed 3/4 part of work in 15 days and A+B complete x/12 part of the work in x days, we can say that :-

3/4 part of work + x/15 part of work = 1 (whole) part of work

Therefore,

x/12 + 3/4 = 1

=> (x+9)/12 = 1

=> x+9 = 12

=> x = 12 - 9

=> x = 3

Hence, A and B work together for 3 days.